You can use the F test to verify a claim about a standard deviation (or variance) for 2 data sets.

Assumptions: The sample is from a "normal distribution"

NOTE: some professors prefer to use the following notation: N~(mean, Standard Deviation)

English Translation: Use an F test  if you are Given: 2 sample sizes (n) and 2 standard deviations (or variances=s² ) AND you are testing a claim about a standard deviation or variance.

Writing the hypothesis:

H₀:  population standard deviation₁ = population standard deviation₂

H₁: population standard deviation₁  is less than, greater than, or not equal to population standard deviation₂

Critical Value = shaded area from F table using the degrees of freedom.

Degrees of freedom: for numerator (use the info from the bigger Standard Deviation) n-1, for denominator (use the info from the smaller Standard Deviation) n-1. Remember that if the null hypothesis requires two tails, split the alpha before using the tables.

Test statistic formula:

F = variance₁ / variance₂

**The bigger variance (standard deviation squared) must be divided by the smaller variance (standard deviation squared).**

Calculator:

Press STAT

Highlight TESTS

Select 2-SampFTest 

Put your information in.

    **NOTE: S₁ must be the biggest standard deviation**

Make sure the not equal to, less than, or greater than symbol matches the one in your alternative hypothesis (H₁).

Highlight Calculate Press ENTER

F is the test statistic, and P is the P-value.

Rejection of the null hypothesis (Ho):

You can reject the null hypothesis if:

• the F from the formula falls in the shaded critical area from the table.
• the P-value is smaller than your alpha Reject Ho.
  

Remember: if you are not given an alpha assume you are using 0.05.